Calling early proficiency with math the “new literacy,” the National Mathematics Advisory Panel says U.S. schools must take steps now to build the foundation for algebra in pre-K to grade 8.
“Most children acquire considerable knowledge of numbers and other aspects of mathematics before they enter kindergarten. This is important because the mathematical knowledge that kindergartners bring to school is related to their mathematics learning for years thereafter–in elementary school, middle school, and even high school,” the panel says after a two-year review of research and policy. The panel heard testimony from 110 individuals.
“Unfortunately, most children from low-income backgrounds enter school with far less knowledge than peers from middle-income backgrounds, and the achievement gap in mathematical knowledge progressively widens throughout their pre-K to 12 years.”
Benchmarks for K-8
To guide the development of students in grades pre-K–8, the panel recommends a set of Benchmarks for the Critical Foundations of Algebra(see table below). The benchmarks should be used to guide classroom curricula, mathematics instruction, textbook development, and state assessments. The panel also developed Major Topics of School Algebra to serve as a focus for curriculum standards, assessments, textbooks and algebra courses.
The Final Report of the National Mathematics Advisory Panel presents 45 recommendations and findings, many of which echo the themes that have been heard in the debate over how U.S. students rank below other countries in international math assessments and what can be done to improve student performance in the future. While the panel made many recommendations focused on boosting readiness for algebra in the elementary and middle school years, it advised that algebra problems involving patterns be “greatly reduced” in state tests and in the National Assessment of Educational Progress.
Below are some highlights from the panel’s recommendations to strengthen U.S. students’ math learning and performance long before they get to high school.
Coherent school math curricula in elementary and middle school years.
Two major differences between U.S. and top-performing countries in international math assessments are the number of mathematical topics presented in each grade and in the expectations for learning, the panel writes.
U.S. curricula should emphasize key topics and be built on a focused, coherent progression in mathematics learning. Continually revisiting topics year after year without closure is to be avoided, the panel says.
Another area of difference between the U.S. and top-performing countries in student math assessments is the integrated approach to teaching math abroad compared with the single-subject approach used in the U.S. Most countries do not follow the typical U.S. sequence of Algebra I, Geometry and Algebra II avoiding the need to continually revisit the same material in teaching. However, after its review of the research, the panel found no basis for favoring one approach over the other.
Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra. A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions). Teachers should be aware of common conceptions and misconceptions involving fractions, based on the scientific literature, and of effective interventions involving fractions, the panel writes. A key mechanism for learning fractions is to be able to represent them on a number line. The curriculum should allow sufficient time to learn fractions which has the broadest and largest impact on problem-solving performance, the panel writes.
Early childhood teacher education.
Teacher education programs and licensure tests for early childhood teachers, including special education teachers, should address whole numbers, fractions, and the appropriate geometry and measurement topics in the Critical Foundations of Algebra, as well as the concepts and skills leading to them.
Content knowledge important for elementary and middle school teacher education.
Research on the relationship between teachers’ mathematical knowledge and students’ achievement confirms the importance of teachers’ content knowledge at this level. Elementary and middle school teachers should have access to preservice teacher education, early career support, and professional development programs for math. Teacher education for middle school teachers, including middle school special education teachers, should address all the Major Topics of School Algebra.
Because most studies have relied on proxies for teachers’ mathematical knowledge (such as teacher certification or courses taken), existing research does not reveal the specific mathematical knowledge and instructional skill needed for effective teaching, especially at the elementary and middle school level. More precise measures are needed to specify in greater detail the relationship among elementary and middle school teachers’ mathematical knowledge, their instructional skill, and students’ learning.
Math specialist teachers.
A number of school districts around the country are using “math specialist teachers” of three different types–math coaches (lead teachers), full-time elementary mathematics teachers, and pull-out teachers. The panel found no high-quality research showing that the use of any of these types of math specialist teachers improves students’ learning, but it recommends more research on this subject. Teachers who specialize in elementary mathematics teaching offer a practical alternative to increasing all elementary teachers’ content knowledge (a problem of huge scale) by focusing the need for expertise on fewer teachers.
Algebra by grade 8.
All school districts should ensure that prepared students have access to an authentic algebra course–and should prepare more students than at present to enroll in such a course by Grade 8. The word authentic is used to describe a course that addresses algebra consistent with the Major Topics of School Algebra developed by the panel.
Math intervention programs.
There have been encouraging results for a variety of instructional programs to improve the mathematical knowledge of preschoolers and kindergartners, especially those from low-income backgrounds. Effective techniques already identified in the research could be put to use in the classroom to improve math learning. More research is needed particularly on larger populations of children from low-income families.
Developmentally appropriate varies with student. Teachers and developers of instructional materials sometimes assume that students need to be a certain age to learn certain mathematical ideas. However, a major research finding is that what is developmentally appropriate is largely contingent on prior opportunities to learn. Claims based on theories that children of particular ages cannot learn certain content because they are “too young,” “not in the appropriate stage,” or “not ready” have consistently been shown to be wrong.
The use of “real-world” contexts to introduce mathematical ideas has been advocated, however, the impact on performance should not be overstated. Research indicates that students who learn math in “real-world” contexts perform better on assessments involving similar “real-world” problems. However, performance on assessments more focused on other aspects of mathematics learning, such as computation, simple word problems, and equation solving, is not improved.
U.S. mathematics textbooks are extremely long–often 700–1,000 pages. One reason for this, according to textbook publishers, is the need to meet the demands of varying state standards. U.S. math textbooks also include many photographs, motivational stories, and other non-mathematical content. Publishers should make every effort to produce shorter and more focused textbooks and to ensure the mathematical accuracy of their materials, the panel says. States and districts should strive for greater agreement on which topics will be emphasized and covered in each grade.
National Mathematics Advisory Panel Final Report, U.S. Department of Education, March 2008.
Published in ERN March 2008 Volume 21 Number 3
|Benchmarks for the Critical Foundations of Algegra
National Mathematics Advisory Panel Final Report, March 2008.Below are benchmarks developed by the National Mathematics Advisory Panel for math learning in Grades 3-7.Fluency with whole numbers By end of Grade 3,